The exact recursion relation for \(R_k\)  following from
Eq. (REF ) was shown
in [1]} to be
\(R_k =\frac{\epsilon +\left( k-1 \right) \left( k-2 \right) k_1}{k_2 - k_1 R_{k+1} +{\bar{k}}_1 R_{k+2} R_{k+1} -\left( k-1 \right)\left(2k_1 - 2 {\bar{k}}_1 R_{k+1}\right) + {\bar{k}}_1\left( k-1 \right) \left( k-2 \right)} .\) 
